I think a lot of the disconnect in the programming world is we treat all programming as equivalent and it's not.
There really are many programming jobs that are rote and I have no problem believing that an LLM based tool can learn the pattern and regurgitate with the tweak de jour. In those jobs LLMs probably do increase productivity.
But there are other programming jobs that are not rote and there is no pattern to learn because you haven't done the thing yet. LLMs aren't any more useful than a normal base library would be, and if you're already good at using a library of code, they're not a productivity booster and often, in my experience, a hinderance.
I think another point is the prompt actually forces the engineer to spend a moment to actually think about what they're doing and make some kind of plan. Pre-AI tools way too many programmers just jumped straight into problems without thinking what they were doing figuring they could code their way out of anything and ending up stuck in some cul de sac and having to back track. And if they just stopped and made a basic plan they wouldn't have that issue. Forcing engineers to make a plan, who wouldn't otherwise do so, before they start, could definitely be a productivity booster for them.